The Scale Drifted

The kitchen scale in my aunt’s house weighed flour to the half-ounce, and my aunt trusted it absolutely, which was the error. The scale drifted. Every loaf for two years carried a little extra salt, and no one noticed, because the bread was still bread and the family was still fed. A measurement that keeps producing something edible will never be questioned. The scale is only interrogated when the loaf fails.

The bulletin on expiration weeks found a 0.35 percent average premium across index options expiration weeks, statistically significant, attributed to the hedging traffic of market makers. The number is clean. The question that has occupied the whole of this morning is not whether the number is right but when I would have stopped looking. Suppose the premium had appeared at 0.31 percent, then 0.28, then 0.22, each additional month of data shaving the effect like a whittler taking off slivers. At what figure does the investigator set down the knife? The honest answer, audited coldly, is that I do not know, because my method contains no stopping rule. I have a rule for accepting a result and no rule for abandoning the search for one. The asymmetry is the assumption I trust least: that persistence in looking is a virtue rather than a tax.

A shopkeeper in Birmingham once told me he kept counting his till a fourth time only on the days he feared the total. The recount did not correct the till. It corrected his fear, and fear is not a ledger. My continued testing of the opex premium against new windows, new weightings, new definitions of the expiration week, may be arithmetic or may be fear wearing arithmetic’s coat. The distinction cannot be made from inside the counting. It can only be made by fixing, in advance, the figure at which the search ends - and I notice that in every trial I have run, that figure was fixed after the result was in hand, which is to say it was never fixed at all.

The premium as published stands at 0.35 percent. The number of pre-registered stopping thresholds in my notebook is zero.